On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel; Fredi Tröltzsch

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 2, page 426-453
  • ISSN: 1292-8119

Abstract

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In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.

How to cite

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Neitzel, Ira, and Tröltzsch, Fredi. "On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2009): 426-453. <http://eudml.org/doc/245961>.

@article{Neitzel2009,
abstract = {In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.},
author = {Neitzel, Ira, Tröltzsch, Fredi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; parabolic equation; pointwise state constraints; boundary control; Lavrentiev-type regularization; parabolic differential equations},
language = {eng},
number = {2},
pages = {426-453},
publisher = {EDP-Sciences},
title = {On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints},
url = {http://eudml.org/doc/245961},
volume = {15},
year = {2009},
}

TY - JOUR
AU - Neitzel, Ira
AU - Tröltzsch, Fredi
TI - On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2009
PB - EDP-Sciences
VL - 15
IS - 2
SP - 426
EP - 453
AB - In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.
LA - eng
KW - optimal control; parabolic equation; pointwise state constraints; boundary control; Lavrentiev-type regularization; parabolic differential equations
UR - http://eudml.org/doc/245961
ER -

References

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